Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Isometric embedding of finite ultrametric spaces in Banach spaces

We prove that for any finite ultrametric space M and any infinite-dimensional Banach space B there exists an isometric embedding of M into B.

Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

On the continuity of the support of masa-bimodules

We anounce results on the continuity of the map sending a masa-bimodule to its support. The proofs of the results will be published elsewhere.

Mid-infrared a-b plane response of YBa2Cu3O7-delta as a function of doping and temperature determined by attenuated total reflection

The mid-infrared optical response of c-axis thin films of YBa2Cu3O7-delta has been studied using Otto-configuration attenuated total reflectance. The measured reflectance-angle characteristics are dominated by a strong absorption feature due to the excitation of surface plasmons, and can be modeled to determine the a-b plane dielectric function. The results show that while epsilon(i,) and therefore sigma(r), are temperature independent, \epsilon(r)\ exhibits a moderate decrease with generalized Drude analysis shows that the plasma frequency is independent of temperature, but decreases with decreasing doping. The scattering rate increases with temperature, and also increases with decreasing doping, consistent with stronger coupling in the underdoped regime. The mass-enhancement is small but increases to 30-40% at delta = 0.6. Difficulties in reconciling the results with some current theories of high-T-c materials are discussed. Finally, the surface plasmon propagation lengths and penetration depths are shown to vary systematically with doping. (C) 2003 Elsevier B.V. All rights reserved.

Temperature dependence of the mid-infrared dielectric function of YBCO in the a-b plane: a re-evaluation

The a-b plane dielectric function (epsilon) of c-axis YBa2Cu3O7-delta thin films with T-c > 85 K was measured at lambda = 3.392 mum in the temperature range 85-300 It, using an attenuated total reflectance (ATR) technique based on the excitation of surface plasmons, The results show that \epsilon (r)\ decreases quasi-linearly with increasing temperature, while Ei is invariant to temperature within experimental uncertainties. Typical values are epsilon (ab) = -23 + 16.5i at similar to 295 R and epsilon (ab) = -27 + 15.5i at similar to 90 K. A generalised Drude analysis yields effective scattering rates (1/tau*) that increase with temperature from similar to 1500 to similar to 1900 cm(-1). The temperature dependent rates best fit an equation of the form 1/tau* = a + bT(alpha) with alpha = 1.46 +/- 0.40. The effective plasma frequencies of w(p)* similar to 18,500 cm(-1) are almost independent of temperature. The uniquely detailed temperature dependence of the results confirm and consolidate data obtained by other groups using normal reflectance methods, but contradict our previously published ATR measurements. Technical shortcomings in the earlier work are identified as the source of the discrepancy. (C) 2000 Elsevier Science B.V. All rights reserved.